The present invention relates to a method of measuring an electrical parameter of a fluid. In particular the present invention concerns the measurement of the electrical conductivity of fluid.
Electrical conductivity is a property of a fluid which may be used in the identification of fluids and in the measurement of the concentration of certain constituents of a solution or mixture of different materials, including bubbles and solids in a fluid medium. The principle of such concentration measurement is that the constituents have a different electrical conductivity as compared to that of the base material, such that the electrical conductivity of the combination varies with the concentration.
Electrical conductivity is measured by passing an electrical current through the fluid and calculating the electrical resistance from the voltage drop across the fluid divided by the current. This is done in a device called a conductivity cell, which contains at least two electrodes separated by the fluid to be measured. The electrical current enters and leaves the fluid by means of electrodes, which are normally arranged so that they are electrically insulated from one another apart from the fluid path.
The electrical conductance is calculated as the inverse of the electrical resistance. Thus, electrical conductance depends not only on the electrical conductivity, but also on the geometry of the electrical path through the fluid and any additional electrical paths (which are normally minimized). In many situations, the conductance C is related to the conductivity P by a simple constant k (which is usually termed the cell constant) as shown in equation 1.
xe2x80x83xcfx81=kcxe2x80x83xe2x80x831
This relationship follows from simple electrical theory, which states that the conductance equals the conductivity times the conductor cross-sectional area divided by the conductor length. In other words, the cell constant equals the conductor length divided by the conductor cross sectional area. Conventionally, the cell constant is established by calibrating the conductivity cell with fluid of known conductivityxe2x80x94typically potassium chloride.
To prevent polarization of the electrodes, whereby an excess (or deficit) of charge builds up at and around the point at which the electrical signal enters and leaves the fluid, alternating current is conventionally used instead of direct current.
Conductivity cells may be arranged to accept a flowing fluid or to measure a static pool of fluid according to the nature of the application.
The conductivity of a fluid depends on temperature and a change of about 2% per degree centigrade is fairly typical. Therefore, in many conductivity measuring devices, a temperature probe is used to measure the temperature, so that a correction may be made for any difference between the actual measurement temperature and the reference temperature (which is often 25xc2x0 C.).
However, accurate temperature compensation is difficult for a number of reasons. The first of these is that the point and time at which the temperature is measured is not (in general) the same point and time at which the conductivity is measured. Thus, any change in the temperature between the temperature measurement and the conductivity measurement results in an error. This problem is exacerbated by the fact that both the temperature measurement and the conductivity measurement usually generate heat as a by product of the measurement technique. At low flow rates, these heating effects have a greater affect on the temperature of the fluid and, at the same time, the temperature probe must be better isolated from the environment to ensure that is neither added nor removed from the fluid by the temperature probe. The lower the flow rate, however, the greater the errors introduced by these problems such that the accuracy which can be obtained with known techniques reduces as the flow rate reduces.
These problems also affect the calibration of the cell when the temperature must also be determined very accurately. This means that the errors are encountered twice in the total measurement process, rather than just at the time of the conductivity measurement of the test fluid. In addition, if the variation of the conductivity with temperature is not accurately known for both the calibration fluid and the test fluid, further errors may be generated in the temperature correction process.
An additional problem with conductivity cells is that the cell constant may change with time and regular re-calibration is required if accurate performance is to be maintained.
PCT Application No. WO-A-9 604 401 discloses methods and apparatus for measuring the differential conductivity of decomposed and undecomposed urea solutions. The present invention is also applicable to such application, and the entire disclosure of WO-A-9 604 401 is incorporated herein by reference thereto.
In accordance with the present invention, these and other objects have now been accomplished by the discovery of a method for measuring an electrical parameter of a test fluid comprising maintaining the test fluid and a reference fluid at substantially the same temperature and in thermal proximity to each other, equalizing the temperature of the test fluid and a reference fluid prior to the measuring step, measuring the electrical parameter of the test fluid and the reference fluid at substantially the same time, and standardizing the measurement to a predetermined temperature. Preferably, measuring of the electrical parameters is carried out in the measurement cell. In a preferred embodiment, the standardizing of the measurement to the predetermined temperature is carried out on the basis of the relationship:
xcfx81b(xcex8)=xcfx81bxcfx81a(xcex8)xe2x88x92xcfx81a)
wherein xcex8 comprises a standard temperature,
xcfx81b(xcex8) comprises the electrical parameter of the test fluid at the standard temperature,
xcfx81a (xcex8) comprises the electrical parameter of the reference fluid at the standard temperature,
xcfx81b comprises the electrical parameter of the test fluid at the measured temperature, and
xcfx81a comprises the electrical parameter of the reference fluid at the measured temperature.
In accordance with one embodiment of the method of the present invention, the reference fluid comprises a calibration fluid.
In accordance with another embodiment of the method of the present invention, the reference fluid is provided by subjecting the test fluid to a predetermined process wherein the electrical parameter is altered. In a preferred embodiment, measuring of the electrical parameter comprises comparing the electrical parameter of a test fluid to the electrical parameter of the reference fluid.
In accordance with a preferred embodiment of the method of the present invention, standardizing of the measurement to the predetermined temperature is determined on the basis of the relationship:
xcfx81b (xcex8)xe2x88x92xcfx81a(xcex8)=xcfx81bxe2x88x92xcfx81a+25(xcex1bxe2x88x92xcex1a)xe2x88x92T(xcex1bxe2x88x92xcex1a)
wherein T comprises the measurement temperature,
xcex1b comprises the temperature coefficient of the electrical parameter of the test fluid, and
xcex1a comprises the temperature coefficient of the electrical parameter of the reference fluid.
In accordance with another embodiment of the method of the present invention, the electrical parameter comprises conductivity. In accordance with another embodiment, the method includes disposing the measurement cell in thermal proximity to flowing primary heat exchange fluid. In a preferred embodiment, the measurement cell is thermally symmetrical about a plane wherein the test fluid and the reference fluid are symmetrically disposed about that plane.
In accordance with another embodiment of the method of the present invention, the method includes providing the primary exchange fluid to the measurement cell and withdrawing the primary heat exchange fluid from the measurement cell in that plane. In accordance with a preferred embodiment, the primary heat exchange fluid and the measurement cell are separated by a metal wall. Preferably, the measurement cell includes a measurement cell plate and the method includes flowing a portion of the primary heat exchange fluid through the metal wall to the measurement cell plate.
In accordance with another embodiment of the method of the present invention, the method includes isolating the measurement cell opposite a region of thermal proximity to the primary heat exchange fluid.
In accordance with another embodiment of the method of the present invention, the method includes flowing the test fluid and the reference fluid through flow paths during the measuring of the electrical parameter.
In accordance with another embodiment of the method of the present invention, the measurement cell comprises a material selected from the group consisting of aluminum and sapphire.
In accordance with another embodiment of the method of the present invention, equalizing of the temperatures of the test fluid and the reference fluid comprises flowing the test fluid and the reference fluid through separate coils of tubing in thermal contact with each other and with a primary heat exchange fluid.
In accordance with another embodiment of the method of the present invention, the method includes measuring at least three portions of the test fluid and the reference fluid.
In accordance with another embodiment of the method of the present invention, the measurement cell comprises a first measurement cell, and the method includes a second measurement cell in parallel with the first measurement cell.
In accordance with the apparatus of the present invention, apparatus is provided for measuring an electrical parameter of a test fluid comprising a measurement cell for receiving the test fluid and a reference fluid, a heat exchanger for maintaining the flow of a primary heat exchange fluid in thermal proximity to the test fluid and the reference fluid, and a metal wall having a first surface and a second surface, the first surface being in contact with the measuring cell and the second surface being in contact with the flow of the primary heat exchange fluid, whereby the measuring cell and the heat exchanger are separated thereby. Preferably, the heat exchanger includes a measuring plate for measuring the electrical parameter, the measuring plate having an exterior, and the heat exchanger maintains the flow of the primary heat exchange fluid over the exterior of the measurement plate.
In accordance with another embodiment of the apparatus of the present invention, the measurement cell is thermally symmetrical about a plane whereby the test fluid and the reference fluid are symmetrically disposed about that plane.
In accordance with another embodiment of the apparatus of the present invention, the measurement cell comprises a first measurement cell, and the apparatus includes a second measurement cell coupled to the heat exchanger.
In accordance with another embodiment of the apparatus of the present invention, the metal wall includes an aperture whereby the primary heat exchange fluid is in direct thermal contact with the measurement cell.
In accordance with another embodiment of the apparatus of the present invention, the apparatus includes a cover for isolating the measurement cell from environmental air.
According to one aspect of the present invention there is provided a method of measuring an electrical parameter of a test fluid comprising the steps of:
(a) providing measurement cell means for separately containing bodies of the test fluid and a reference fluid, the bodies being at substantially the same temperature and in thermal proximity to each other,
(b) equalizing the temperatures of these fluids prior to introducing them into the measurement cell means,
(c) measuring the electrical parameter of the body of test fluid and the body of reference fluid at substantially the same time, and
(d) standardizing the measurement to a predetermined temperature on the basis of the relationship:
xcfx81b (xcex8)=xcfx81b(xcfx81a(xcex8)xe2x88x92xcfx81a).
xe2x80x83where: xcfx81b(xcex8) is the electrical parameter of the test fluid at a standard temperature xcex8,
xcfx81a(xcex8) is the electrical parameter of the reference fluid at standard temperature xcex8,
xcfx81b is the electrical parameter of the test fluid at the measurement temperature,
xcfx81a is the electrical parameter of the reference fluid at the measurement temperature,
xcex1b is the temperature coefficient of the electrical parameter of the test fluid, and
xcex1a is the temperature coefficient of the electrical parameter of the reference fluid.
When the temperatures of the test fluid and reference fluid are equalized prior to measurement, temperature related errors in the measurement can be reduced.
In one embodiment of the method of the present invention, the reference fluid has a known value of the parameter and is used as a calibration fluid to calibrate the measurement of the electrical property of the test fluid.
In another embodiment of the method of the present invention, a differential measurement is made and it is not necessary for the parameter of the reference fluid to be known.
Preferably, the method of the present invention further comprises placing the test fluid and the reference fluid in separate cells which are in thermal contact and more preferably comprises a further step of passing the test fluid and reference fluid through a pair of secondary coils in a heat exchanger to ensure thermal equilibrium of the fluids. The reference fluid preferably undergoes a modification step which alters the electrical property of the reference fluid, and preferably the reference fluid is the same as the test fluid.
In another aspect, the present invention provides apparatus for determining an electrical parameter of a test fluid in relation to that of a reference fluid, comprising test cell means arranged to receive a body of the test fluid and a body of the reference fluid and heat exchange means for generating a flow of primary heat exchange fluid in thermal proximity to the bodies of test fluid and reference fluid, the heat exchange means comprising a metal wall having one surface in contact with the measurement cell means and an opposite surface in contact with the flow of primary heat exchange fluid, whereby the measurement cell means is outside the heat exchange means.
Rather than attempting to measure the temperatures of the calibration fluid and the test fluid accurately, the electrical conductivities of the two fluids are preferably measured at essentially the same time as each other using a pair of cells which are in close thermal proximity to one another, such that a substantial temperature difference cannot exist between them. Most of the temperature related errors then cancel out and there is no heating generated by the temperature measurement.
Preferably the measurement cell means is thermally symmetrical about a plane midway between the bodies of test fluid and reference fluid, the bodies being symmetrically disposed about the plane.
To ensure that the temperatures of the two fluids are the same as each other as they enter their respective cells, they may optionally be passed through a pair of secondary coils of a heat exchanger, which is preferably also used to control the temperature of the cells. The temperature of the fluid in the cells can be measured indirectly by measuring the temperature of the fluid in the primary flow path of the heat exchanger. The flow rate through the primary path can generally be higher because the primary fluid can be recirculated, whereas the test fluid is often only available in limited quantities. This means that the temperature can be measured more readily without the limitations described above.
As noted above, two preferred modes of operation are possible, namely one in which the reference fluid is a calibration fluid, whose electrical conductivity has been characterized under exacting conditions, with ample quantities and time for each measurement, and a second in which a differential measurement is made. This differential mode is particularly relevant when a fluid can be split into two paths, with the conductivity of one path being modified by some process before the conductivities of both paths are compared. In this case, the important factor is the change caused by processing one path (rather than the absolute value of the conductivity).
In the first case, the temperature need not be measured (directly or indirectly) as shown by the following analysis:
The electrical conductivity of cell a can be represented by the following equation:
xcfx81a=xcfx81a25+xcex1a(Taxe2x88x9225)xe2x80x83xe2x80x832
where xcfx81a=measured electrical conductivity in cell a
Ta=temperature in cell
xcfx81a25=electrical conductivity of fluid in cell a at 25xc2x0 C.
xcex1a=rate of change of electrical conductivity with temperature
This is the equation used with single cell conventional measurements and it will be appreciated that an error in the temperature measurement leads directly to an error in the conductivity.
For twin cell measurement, a similar equation can be written for the second cell, as follows:
xcfx81b=xcfx81b25+xcex1b(Tbxe2x88x9225)xe2x80x83xe2x80x833
where xcfx81b=measured electrical conductivity in cell b
Tb=temperature in cell
xcfx81b25=electrical conductivity of fluid in cell b at 25xc2x0 C.
xcex1b=rate of change of electrical conductivity with temperature
Provided the temperatures Ta and Tb are equal, these two equations can be combined to provide an expression for the conductivity of the fluid in cell b in terms of the two cell measurements and the known properties, but without knowledge of the temperature. Thus, the conductivity of the fluid in cell b referred to 25xc2x0 C. is:
xcfx81b25=xcfx81b+(xcfx81a25xe2x88x92xcfx81a) xcex1b/xcex1axe2x80x83xe2x80x834
For the second mode of operation, the differential referred to 25xc2x0 C. (xcfx81b25xe2x88x92xcfx81a25) can be found, again provided Ta=Tb, as follows:
xcfx81b25xe2x88x92xcfx81a25=xcfx81bxe2x88x92xcfx81a+25(xcex1bxe2x88x92xcex1a)xe2x88x92T(xcex1bxe2x88x92xcex1a)xe2x80x83xe2x80x835
Although this is not completely independent of temperature, the accuracy with which the temperature must be known is less than for a single cell device, because xcex1b and xcex1a are normally equal or very close to each other. This means that the indirect temperature measurement technique described above is particularly suitable.
A similar analysis is applicable to the measurement of other electrical parameters, for example capacitance or dielectric loss tangent.
The use of two cells in the same device also allows for re-zeroing of the two cells against each other. This means that changes in the cell constant can be detected and a compensation made without the need for a re-calibration.
As previously mentioned, the two cells are preferably in close thermal proximity to each other and this is best achieved by making them from a material with a high thermal conductivity, but low electrical conductivity, to ensure that the electrodes are insulated from each other (except for the path through the fluid). Particularly suitable materials are alumina ceramic and sapphire or metals with an insulating coating such as glass. Close thermal proximity can also be enhanced by making the distance between the flows paths of the cells small and by making the entire construction symmetrical with respect to heat flows, so that there is no significant heat flow from one cell to the other (which would cause a temperature difference). Furthermore, the entire cell assembly should preferably be placed in close thermal proximity to the primary side of the heat exchanger by attaching the cells to a thermally conductive wall of the heat exchanger.
It will be understood that the measurement of the conductance of the electrical path through the fluid in the cell is achieved by conventional means and as such is not described in detail.